A reconstruction theorem for locally moving groups acting on completely metrizable spaces

Edmund Ben-Ami. "A reconstruction theorem for locally moving groups acting on completely metrizable spaces." Fundamenta Mathematicae 209.1 (2010): 1-8. <http://eudml.org/doc/282592>.

@article{EdmundBen2010,
abstract = { Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category in Y, then X and Y are homeomorphic. A particular case of Theorem A gives a positive answer to a question of M. Rubin and J. van Mill who asked whether X and Y are homeomorphic whenever G is strongly locally homogeneous on X and Y. },
author = {Edmund Ben-Ami},
journal = {Fundamenta Mathematicae},
keywords = {groups of homeomorphisms; locally moving group; reconstruction problems; complete metric spaces},
language = {eng},
number = {1},
pages = {1-8},
title = {A reconstruction theorem for locally moving groups acting on completely metrizable spaces},
url = {http://eudml.org/doc/282592},
volume = {209},
year = {2010},
}

TY - JOUR
AU - Edmund Ben-Ami
TI - A reconstruction theorem for locally moving groups acting on completely metrizable spaces
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 1
SP - 1
EP - 8
AB - Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category in Y, then X and Y are homeomorphic. A particular case of Theorem A gives a positive answer to a question of M. Rubin and J. van Mill who asked whether X and Y are homeomorphic whenever G is strongly locally homogeneous on X and Y.
LA - eng
KW - groups of homeomorphisms; locally moving group; reconstruction problems; complete metric spaces
UR - http://eudml.org/doc/282592
ER -